A method for estimating the road gradient is conventionally proposed, for example, as disclosed in Japanese Patent Publication No. H02-161308, according to which the road gradient is estimated based on vehicle acceleration in a vehicle longitudinal direction detected by an acceleration sensor provided on a vehicle as well as acceleration of the vehicle with respect to the road. The acceleration of the vehicle with respect to the road is, for example, acceleration for a component of gravity (which corresponds to the road gradient), which is calculated based on a time varying value (differentiated value) of a vehicle wheel speed detected by a wheel speed sensor.
More exactly, the road gradient “θ” is calculated in the following formula (1). This is based on an idea that a value subtracting a time varying portion “A′” of a wheel speed from a vehicle acceleration in the vehicle longitudinal direction corresponds to the acceleration for the component of gravity. In the formula (1), “g” is the acceleration of gravity, and “θ” is the road gradient.θ=sin−1 {(A−A′)/g}  (1)
The road gradient thus calculated is applied to, for example, a vehicle cruise control system or a vehicle distance control system (an adaptive cruise control system), and furthermore used as a calculation parameter for braking force in a vehicle braking force control for a pre-crash system.
However, the above detected acceleration may include various kinds of disturbance parameters, such as variation of acceleration having noise generated when the vehicle climbs over a foreign substance existing on the road, variation of acceleration caused by road undulation, and soon. Accordingly, the road gradient calculated in the above manner is not always sufficiently accurate. It is, therefore, necessary to estimate the road gradient more accurately, in order to achieve optimization for a vehicle behavior control (a control for a vehicle driving force as well as a vehicle braking force).